# Propability of finding a particle outside the classical limit

1. May 18, 2015

### Noctisdark

1. The problem statement, all variables and given/known data
I'm asked to calculate the propability of finding a particle outside the classical limit for a quantum harmonic oscillator in it's ground state

2. Relevant equations
Ψ0(x) = a*emωx2/2hbar
When a = (mω/πhbar)1/4
The ground state energy E0 =hbar*ω2/2
3. The attempt at a solution
I actually don't know what to do, I've tried to consider it as tunelling by finding when the energy is equal to the potential
E0 = hbar*ω2/2 = mω2x2, and stuck there !

2. May 18, 2015

### TSny

You might start by finding the amplitude, $A$, of oscillation for a classical oscillator with energy E0. The quantum oscillator is "outside the classical limit" when x is outside the range $-A\leq x \leq A$.

I don't understand this equation. Why is $\omega$ squared in the middle expression. I also don't understand the meaning of the expression on the right.

I think you have a typo in the expression for the wavefunction. The argument of the exponential should be negative.

Last edited: May 18, 2015